**Unformatted text preview: **of N ) the ratio of height to base radius of the cylinder that minimizes the cost of making the containers. Let us ﬁrst choose letters to represent various things: h for the height, r for the base radius, V for the volume of the cylinder, and c for the cost per unit area of the lateral side of the cylinder; V and c are constants, h and r are variables. Now we can write the cost of materials: c (2 πrh ) + Nc (2 πr 2 ) . Again we have two variables; the relationship is provided by the ﬁxed volume of the cylinder: V = πr 2 h . We use this relation to eliminate h (we could eliminate r , but it’s a little easier if we eliminate h , which appears in only one place in the above formula for cost). The result is f ( r ) = 2 cπr V πr 2 + 2 Ncπr 2 = 2 cV r + 2 Ncπr 2 ....

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- Fall '07
- JonathanRogawski
- Math, Calculus, Derivative, unit area